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Estimation procedures for exchangeable Marshall copulas with hydrological application

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  • Fabrizio Durante
  • Ostap Okhrin
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    Abstract

    Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called exchangeable Marshall copulas. Such copulas describe both positive and (upper) tail association between random variables. Speci cally, inference procedures for the family of exchangeable Marshall copulas are introduced, based on the estimation of their (univariate) generator. Moreover, the performance of the proposed methodologies is shown in a simulation study. Finally, an illustration describes how the proposed procedures can be useful in a hydrological application.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2014-014.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2014-014.

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    Length: 30 pages
    Date of creation: Jan 2014
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    Handle: RePEc:hum:wpaper:sfb649dp2014-014

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    Related research

    Keywords: Copula; Kendall distribution; Marshall-Olkin distribution; Non-parametric Estimation; Risk Management;

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    1. Fabrizio Durante, 2009. "Construction of non-exchangeable bivariate distribution functions," Statistical Papers, Springer, Springer, vol. 50(2), pages 383-391, March.
    2. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter Open, De Gruyter Open, vol. 1, pages 1-36, October.
    3. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Penev, Spiridon I., 2008. "GeD spline estimation of multivariate Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 52(7), pages 3570-3582, March.
    4. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 99(10), pages 2234-2250, November.
    5. Manner, Hans & Segers, Johan, 2011. "Tails of correlation mixtures of elliptical copulas," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 153-160, January.
    6. Jean-François Quessy, 2012. "Testing for Bivariate Extreme Dependence Using Kendall's Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(3), pages 497-514, 09.
    7. Christian Hering & Jan-Frederik Mai, 2012. "Moment-based estimation of extendible Marshall-Olkin copulas," Metrika, Springer, Springer, vol. 75(5), pages 601-620, July.
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